For models where the tire and rim come as one part I normally do the following:
1.) Paint the rim.
2.) Draw a dividing line where the rim and tire join, use a small permament marker or ink-pen for this.
3.) Paint the tire along the line I drew, visual guides make the job a lot easier.
With the line you don't need to bring the brush that close to the rim.
4.) Make sure that you don't have too much paint on the brush.
This works well for Plane are car-tires, which are normally painted either Gunze Tire Black or a mix of Tamiya colours.